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Front. Inform. Technol. Electron. Eng.  2012, Vol. 13 Issue (5): 393-402    DOI: 10.1631/jzus.C1100313
    
Numerical solution of potential flow equations with a predictor-corrector finite difference method
Zhi-qiang Luo
Department of System Science and Applied Mathematics, School of Science, Kunming University of Science and Technology, Kunming 650083, China
Numerical solution of potential flow equations with a predictor-corrector finite difference method
Zhi-qiang Luo
Department of System Science and Applied Mathematics, School of Science, Kunming University of Science and Technology, Kunming 650083, China
 全文: PDF 
摘要： We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition. A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank. The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function. A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid. The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition. We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion, and the numerical solutions of wave elevation with horizontal excited motion. The beating period and the nonlinear phenomenon are very clear. The numerical solutions agree well with the analytical solutions and previously published results.
关键词： Predictor-corrector method;  Nonlinear potential flow equations;  Finite difference method;  Staggered grid;  Nested iterative method    
Abstract: We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition. A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank. The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function. A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid. The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition. We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion, and the numerical solutions of wave elevation with horizontal excited motion. The beating period and the nonlinear phenomenon are very clear. The numerical solutions agree well with the analytical solutions and previously published results.
Key words: Predictor-corrector method    Nonlinear potential flow equations    Finite difference method    Staggered grid    Nested iterative method
收稿日期: 2011-10-26 出版日期: 2012-05-03
CLC:  O24  
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引用本文:

Zhi-qiang Luo. Numerical solution of potential flow equations with a predictor-corrector finite difference method. Front. Inform. Technol. Electron. Eng., 2012, 13(5): 393-402.

链接本文:

http://www.zjujournals.com/xueshu/fitee/CN/10.1631/jzus.C1100313    或    http://www.zjujournals.com/xueshu/fitee/CN/Y2012/V13/I5/393

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